R Notebook

Generate state or county level output

Plot the epidemic timecourse from simulations vs data

Summed over all states

Using the final output from each simulation

Fig. 1 Model calibration to incident cases (A) and incident deaths (B) reported by JHU CSSE for each state at 0.5% IFR assumptions, summed over entire country. Shaded areas show 95% confidence intervals based on independent inference runs and black points/lines indicate data reported by JHU CSSE.

For each state

(for subset of states only now)

Fig. 2 Calibration of estimated incident cases and deaths to reported data from JHU CSSE, and validation of estimates for occupied hospital beds when compared to CDPH data. Here, modeled cases are calculated as a percent of modeled infection that is fit to county data. Black points represent actual data, lines represent means and shading represents the 95% prediction interval for each scenario at 0.5% IFR and 0.5% assumptions. Note that JHU CSSE data were reported as daily cumulative cases and deaths. In this figure, daily cumulative case counts were differenced in order to report the incident cases and deaths. In comparing the actual and modeled data, we emphasize that limited testing and reporting delays may affect the quality of the reported case data early on in the outbreak.

Plot the likelihood by MCMC iteration - global, and chimeric for each state

Fig. 3 GeoID-specific log-likelihood values by MCMC step. Here ‘chimeric’ values are the likelihood for accepted parameters in the chimeric likelihood, and ‘global’ values are the likelihood values for the proposed parameters of the chimeric likelihood, which are recorded in the global likelihood files. These two likelihood values are equivalent only at steps where the chimeric likelihood was accepted for that GeoID.**

Same but for combined national likelihood

Fig. 4 Total log-likelihood values by MCMC step (summed over all GeoIDs). Here ‘chimeric’ values are the total likelihood for accepted parameters in the chimeric likelihood, and ‘global’ values are the likelihood values for the proposed parameters of the chimeric likelihood, which are recorded in the global likelihood files. The chimeric (accepted) likelihood is always higher since acceptance decisions are made on a geoID-by-geoID level, and only accepted for GeoIDs where the acceptance would improve the geoID-specific likelihood. These two likelihood values would only be equivalent at steps where the chimeric likelihood was accepted for every single GeoID.**

Look at proportion of likelihoods accepted or rejected

Plot chimeric acceptance rates for each state, rolling mean over all previous iterations (saved in chimeric intermediate likelihood files)

Plot when global acceptances occurred

Fig. 5 Acceptance rate of proposed parameters by MCMC step for each state (‘chimeric’ values) along with the global acceptance rate. Acceptance rate is averaged over all previous steps. **

Now plot average acceptance as rolling mean over an interval

Fig. 6 Acceptance rate of proposed parameters by MCMC step for each state (‘chimeric’ values) along with the global acceptance rate. Acceptance rate is averaged over the previous25steps**

Plot cumulative acceptances

Fig. 7 Cumulative number of acceptances of proposed parameters by MCMC step for each state (‘chimeric’ values) along with the global acceptance rate**

Plot all infered parameter values by MCMC iteration for a given state

Look at basic SEIR parameter values

These are the same for all states, and are fixed, not estimated, so nothing to plot

Fig. 8 SEIR parameters by MCMC step (‘chimeric’ values) along with the global acceptance rate**

Look at outcome model parameter values

These are the same for all states, and are fixed, not estimated, so nothing to plot

Fig. 9 Inferred outcome parameter values by MCMC step for each GeoID.’Global’ values are the proposed parameters at each step, and ‘Chimeric’ values are the parameters accepted at the GeoID-level in the chimeric likelihood **

Look at intervention effects

SNPI (NPIs acting on SEIR values)

Including local variance in R0

Fig. 10 Inferred paramter values by MCMC step for each GeoID.’Global’ values are the proposed parameters at each step, and ‘Chimeric’ values are the parameters accepted at the GeoID-level in the chimeric likelihood **

Should repeat this for HNPI parameter values

(no interventions on outcome parameters in these simulations, so files are empty and can’t be opened with arrow)

Look at correlations between different fit parameter values, for each state

Update this to combine fit parameters of different types (snpi, hnpi, spar, hpar, etc)

### Do an extra analysis calculating the average correlation over all states and plotting

Look at variance of each parameter from the posterior and compare to the proposal step size

This is a way of measuring whether adaptive MCMC could help. (Ignore covariance for now). If observed std >> perturb_sd, suggests that proposal too small. If observed_sd << perturb_sd, suggests proposal too big